Distance from Point to 3D Plane

Question

Find the distance from the point Q = (1,3,1) to the plane 2x+5y-z=8.

I got 17/ sqrt(30) but this is incorrect.

If you could explain the steps you take to get to your answer, it would be appreciated!

Answer 1

you find the plane parallel to the given plane that contains Q, (1, 3, 1). Then, it is easy to find how apart the 2 planes are.

2x + 5y - z = 2(1) + 5(3) - 1(1) = 16

Thus, the point is on 2x + 5y - z = 16

Then, as the other plane is 2x + 5y - z = 8, the planes are |16 - 8|/sqrt(2^2 + 5^2 + (-1)^2) = 8/sqrt(30) or

4 sqrt(30)/15